PIN Diode

1. Theory

• Definition: A PIN diode has a wide, lightly doped (nearly intrinsic) i-layer sandwiched between heavily doped ${\mathrm{P}}^{+}$ and ${\mathrm{N}}^{+}$ regions.
• Intrinsic layer: The i-region’s residual doping is so low that it fully depletes at a small reach-through voltage, so its physical thickness fixes the depletion width.
• Uniform field: The field across the depleted i-region is nearly uniform rather than triangular, so breakdown voltage scales roughly linearly with i-layer thickness.
• Conductivity modulation: Under forward bias, electrons and holes injected from both ends flood the i-region as a dense plasma, greatly lowering its resistance.
• Stored charge: The forward current sustains a stored charge in the i-region, set by the forward current and the ambipolar carrier lifetime.

2. Working Principle

• Reverse bias: Beyond reach-through the i-region is fully depleted, giving a small, nearly bias-independent capacitance; at RF the diode looks like a small capacitor (off state).
• Forward bias: The injected plasma gives a current-controlled resistance that falls inversely with forward current (on state).
• RF behaviour: When the carrier lifetime is much longer than the RF period, the stored charge cannot follow the signal, so the diode does not rectify and acts as a linear resistor set by the DC bias.
• High breakdown: The wide, uniformly stressed i-layer supports large reverse voltages.
• Switching trade-off: A long lifetime lowers on-resistance, but more stored charge must be removed at turn-off, increasing the reverse recovery time.
• Photodetection: Photons absorbed in the wide depleted i-region create electron-hole pairs that are swept out by drift, giving high quantum efficiency and fast response.

3. Applications

• RF and microwave switches: Standard high-power switching element for antenna and transmit-receive switching.
• Variable attenuators and phase shifters: Bias-controlled RF resistance gives continuous attenuation and phase control.
• RF limiters: Self-biased PIN diodes protect sensitive receiver inputs from high-power signals.
• Photodiodes: Main detector in fibre-optic receivers, where speed and efficiency matter.
• High-voltage power rectifiers: The ${\mathrm{P}}^{+}$-${\mathrm{N}}^{-}$-${\mathrm{N}}^{+}$ structure is the basis of bipolar power rectifiers at voltages too high for Schottky diodes.
• Radiation detectors: Fully depleted silicon PIN diodes detect X-rays and charged particles.

Name	Formula	Related Formulae	Variables/Constants
Built-in potential (contact potential)	$V_{bi}=\frac{k_{B}T}{q}\ln \left(\frac{N_A{N}_D}{n_i^2}\right)$	$n_i^2=N_C{N}_V\exp \left(-\frac{E_g}{k_{B}T}\right)$	$\begin{array}{r}{V}_{bi}:built-inpotentialacross\\ the{p}^{+}-n^{+}regions\end{array}$ $N_A,N_D:p^{+}and{n}^{+}contactdopingconcentrations$ $n_i:intrinsiccarrierconcentration$ $k_B:Boltzmannconstant$
Reach-through (full depletion) voltage	$V_{RT}\approx \frac{q{N}_i{W}_i^2}{2{\epsilon }_s}$	$x_{p^{+}},x_{n^{+}}\ll W_i\text{(negligible depletion in the}{p}^{+},n^{+}\text{regions)}$	$\begin{array}{r}{V}_{RT}:voltageatwhichthe\\ i-regionbecomesfullydepleted\end{array}$ $\begin{array}{r}{N}_i:residual(unintentional)background\\ dopingofthe"intrinsic"layer\end{array}$ $W_i:intrinsiclayerthickness$
Depletion (junction) capacitance	$C_j\approx \frac{{\epsilon }_{s}A}{W_i}(V>V_{RT})$	$C_j=\frac{{\epsilon }_{s}A}{W}\text{(general step-junction form)}$	$\begin{array}{r}{C}_j:depletioncapacitance,nearly\\ bias-independentoncethe\\ i-regionisfullydepleted\end{array}$ $A:junctioncross-sectionalarea$
Stored charge in the intrinsic region (forward bias)	$Q=I_F\tau$	$p_{avg}=\frac{Q}{qA{W}_i}$	$\begin{array}{r}Q:totalinjectedcarrierchargestored\\ inthei-region\end{array}$ $I_F:forwardcurrent$ $\begin{array}{r}\tau :ambipolarcarrierlifetimeinthe\\ i-region\end{array}$ $p_{avg}:averageinjectedcarrierdensity$
Forward (charge-controlled) resistance of the i-region	$R_S=\frac{W_i^2}{({\mu }_n+{\mu }_p)Q}$	$Q=I_F\tau$	$\begin{array}{r}{R}_S:small-signalresistanceofthe\\ forward-biasedi-region\end{array}$ $\begin{array}{r}{\mu }_n,{\mu }_p:electronandhole\\ mobilitiesintheintrinsiclayer\end{array}$
Carrier transit time across the i-region	${\tau }_{tr}=\frac{W_i^2}{2D_a}$	$D_a=\frac{2D_n{D}_p}{D_n+D_p}$	$\begin{array}{r}{\tau }_{tr}:meantransittimeofinjected\\ carrierscrossingthei-region\end{array}$ $D_a:ambipolardiffusioncoefficient$
RF cutoff frequency	$f_c=\frac{1}{2\pi R_S{C}_j}$		$\begin{array}{r}{f}_c:figure-of-meritcutoff\\ frequencyforRFswitch/attenuator\\ operation\end{array}$
Reverse breakdown voltage (near-uniform field approximation)	$BV\approx E_{crit}{W}_i$	$B{V}_{step}\approx \frac{{\epsilon }_s{E}_{crit}^2}{2q{N}_B}\text{(contrast: one-sided step junction, PN diode page)}$	$BV:reversebreakdownvoltage$ $\begin{array}{r}{E}_{crit}:critical(breakdown)electricfield,\\ material-dependent\end{array}$
Reverse recovery time	$t_{rr}\approx \tau \ln \left(1+\frac{I_F}{I_R}\right)$	$Q=I_F\tau$	$t_{rr}:reverserecoverytime$ $I_R:reversecurrentduringturn-off$

Important Questions

Ques: Why is PIN diode junction capacitance nearly constant with reverse bias, unlike a standard PN diode?

In a PN step junction, $C_j\propto (V_{bi}-V{)}^{-1/2}$ because the depletion width keeps growing into both doped regions as reverse bias increases. In a PIN diode, the lightly doped “intrinsic” layer has such a low residual doping $N_i$ that it fully depletes at a very small reach-through voltage $V_{RT}$; beyond that point, the depletion region is pinned at the fixed physical width $W_i$ of the i-layer and cannot grow any further (the heavily doped $p^{+}$ and $n^{+}$ regions barely deplete at all), so $C_j\approx {\epsilon }_{s}A/W_i$ stays essentially constant over the diode’s entire useful reverse-bias range. This near-constant, deliberately low capacitance is precisely why PIN diodes are chosen over PN diodes for RF and microwave applications. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Ques: Why does a PIN diode behave like a variable resistor under forward bias instead of following the exponential Shockley I-V law like a PN diode?

Under forward bias, electrons and holes are injected into the intrinsic region in roughly equal, high concentrations (an ambipolar plasma), since there is no background doping to set a fixed majority-carrier population the way there is in a conventional PN diode’s quasi-neutral regions. The resulting conductivity of the i-region is set by this injected carrier density, which in turn is controlled by the forward current through the stored charge $Q=I_F\tau$, giving a resistance $R_S$ that varies smoothly and continuously with $I_F$ rather than exhibiting the sharp exponential turn-on of a conventional diode junction. This charge-controlled-resistance behavior is exactly what makes PIN diodes useful as electronically variable RF attenuators and switches. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007; general RF/microwave PIN diode switch design references.

Ques: Why does PIN diode breakdown voltage scale roughly linearly with $W_i$ instead of the quadratic-in-doping relation used for a step junction?

Because the field across a fully depleted, lightly doped i-region is nearly uniform (rather than triangular and sharply peaked as in a one-sided step junction), the breakdown condition is reached when that nearly-constant field equals the critical field $E_{crit}$ across the entire width $W_i$, giving $BV\approx E_{crit}{W}_i$ — a linear relationship. This is the key structural advantage of the PIN diode: widening the intentionally undoped i-layer buys roughly proportional increases in breakdown voltage without the steep doping-dependent tradeoffs a step junction faces, which is why PIN structures are also used in high-voltage power rectifiers and photodiodes, not just RF switches. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007.

Related pages in this vault: Schottky Diode, PN Junction, GaN Power Diode, Step Recovery Diode, PIN Photodiode, Diodes (PN, PIN, Schottky, Zener), Silicon Carrier-Injection PIN Modulator, Power Device Compact Models, Diode Compact Models.